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研究生： 林凌豪
Lin, Lin-Hao
論文名稱： 雙黑洞在星系重力場下的速度比之研究
The Study on the Velocity Ratio of Binary Black Holes with Galactic Potential
指導教授： 葉麗琴
Yeh, Li-Chin
口試委員: 江瑛貴
Jiang, Ing-Guey
陳賢修
Chen, Shyan-Shiou
學位類別： 碩士
Master
系所名稱： 理學院 - 計算與建模科學研究所
Institute of Computational and Modeling Science
論文出版年： 2023
畢業學年度： 111
語文別： 英文
論文頁數： 43
中文關鍵詞： 雙黑洞系統 、黑洞動力學 、速度比
外文關鍵詞： binary black hole, black hole dynamics, velocity ratio
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    • 在本論文中，主要探討雙黑洞動態系統在星系重力場的影響下，速度比與質量比之間的關係。在天文學的研究裡，普遍認為活躍星系核中心是超大質量黑洞。Wang et al. [11] 在雙活躍星系核的研究中，發現雙活躍星系核速度比與質量比之間有著顯著的相關性。因此，在考慮星系重力場的影響下，我們提供不同初始條件的雙黑洞模型，對速度比與質量比的關係進行研究。

    In this thesis, we primarily study the relationship between velocity ratio and mass ratio in the binary black holes with galactic potential. In the field of astronomy, it is widely accepted that the center of active galactic nuclei hosts supermassive black hole. In the study of dual active galactic nuclei (AGNs), Wang et al. [11] discovered a significant correlation between the velocity ratio and mass ratio of
    dual AGNs. Therefore, considering the influence of galactic potential, we explore the relationship between velocity ratio and mass ratio by choosing different initial conditions in binary black holes models.

    摘要 . . . . . . . . . . . . . . . . . . i Abstract . . . . . . . . . . . . . . . ii Chapter 1 Introduction . . . . . . . . . . . . . . . . 1 Chapter 2 Analytical Formulas . . . . . . . . . . . . .3 2.1 Circular Orbit . . . . . . . . . . . . 3 2.2 Elliptical Orbit . . . . . . . . . . . 7 Chapter 3 The Orbit Behaviors of Supermassive Binary Black Hole in Galaxical Potential . . . . . . . . . . . . . . . . . .14 3.1 Equations of Motion . . . . . . . . . . . . . 16 3.2 c = 0 Case with a circular orbit . . . . . . 19 3.3 c ̸= 0 Case with elliptical orbits . . . . . 22 3.3.1 Equal mass case . . . . . . . . . . . 22 3.3.2 Unequal masses cases . . . . . . . . .24 3.3.3 Different total mass of galaxy . . . .31 Chapter 4 Conclusion . . . . . . . . . . . . . . . . . .33 A Kepler’s Laws of Planetary Motion . . . . 34 A.1 Kepler’s 2nd Law . . . .34 A.2 Kepler’s 1st Law . . . .36 A.3 Kepler’s 3rd Law . . . .39 B Three Dimensional Transformation . . . . .41 Reference . . . . . . . . . . . . . . . . . . . . . . . .43

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